Mathematical models of cancer growth have become increasingly more accurate both in the space and time domains. However, the limited amount of data typically available has resulted in a larger number of qualitative rather than quantitative studies. In the present study, we provide an integrated experimental-computational framework for the quantification of the morphological characteristics and the mechanistic modelling of cancer progression in 3D environments. The proposed framework allows for the calibration of multiscale, spatiotemporal models of cancer growth using state-of-the-art 3D cell culture data, and their validation based on the resulting experimental morphological patterns using spatial point-pattern analysis techniques. We applied this framework to the study of the development of Triple Negative Breast Cancer cells cultured in Matrigel scaffolds, and validated the hypothesis of chemotactic migration using a multiscale, hybrid Keller-Segel model. The results revealed transient, non-random spatial distributions of cancer cells that consist of clustered, and dispersion patterns. The proposed model was able to describe the general characteristics of the experimental observations and suggests that chemotactic migration together with random motion was found to be a plausible mechanism leading to accumulation, during the examined time period of development. The developed framework enabled us to pursue two goals; first, the quantitative description of the morphology of cancer growth in 3D cultures using point-pattern analysis, and second, the relation of tumour morphology with underlying biophysical mechanisms that govern cancer growth and migration.